If you are using fresh broccoli, steam in a steamer until just done. Follow the directions on your steamer, or steam with a pot and a steamer insert. This takes 5 to 7 minutes.
In a medium saucepan, cook the onion in the butter until transparent. Add the cheese, soup, broccoli, and rice to the onions and stir through to melt the cheese and heat it all. You can serve this dish now, or you can put it in an 8-inch square baking pan, cover, and refrigerate. When you are ready to serve, uncover and reheat it in a 350 degree F oven for about 20 minutes, until hot and bubbly.